Before i go into whats next I must address something in this thread. Until the field interacts with something in it, it's force carriers are virtual. Once interacting with matter, the field of vitual particles can produce real particles which may or may not be directed in thier motion by the field depending on whether the particles carry the sources of the field.

"Now, the force carriers cannot be affected by the force they carry (i.e., a photon cannot exhibit an electromagetic charge- it only CARRIES it). So, by symmetry a graviton cannot be affected by the gravitational force. "

There is a lack of symmetry here. The poisson equation for the electric potential is linear. The poisson equation(Einstein's field equations) for the gravitational potential(the metric tensor) is nonlinear. Yes, if photons carried charge i.e. their paths were to be affected by the field, then the electic poterntial's poisson equation would also have to be nonlinear. Gravitons do act as carrying momentum/energy which are sources in the Einstein field equations as well as the something that is altered by the field through geodesic motion, but we expect this because of the nonlinear nature of the gravitational field's poisson equation.